D.B.
There are some classic stories and lessons in dealing with gossip - and remember that "gossip" is defined as something spread about another person whether or not the information is true. That's an important distinction.
Some books/stories include "A Pillow Full of Feathers" is the Jewish version, but "Feathers in the Wind" and "A Sackful of Feathers" are from (I think) a Catholic perspective. (At least one of them deals with St. Philip Neri.) There are probably secular versions as well. In any case, the story is that a wise person has a child or an adult take an old feather pillow, open it up, shake out the feathers and then try to retrieve and replace the feathers. Of course, the person realizes it's impossible and the wise person says, "That's how it is with gossip and rumor - it's easy to distribute and impossible to take back."
Another example is squirting some toothpaste out of the tube and saying it's too much, and could your daughter please put some of it back in the tube. Of course, that's impossible as well.
I think, but her age, you could expand this to topics of sexting and saying things on social media - it's out there forever.
Finally, when I was teaching in a small school, we had a big poster that said THINK. It was to contain gossip but also things like calling out in class or correcting another student. It stands for:
T - Is it true?
H - Is it helpful?
I - Is it inspiring?
N - Is it necessary?
K - Is it kind?
Also, there are some great books on gossip, why people do it, and what it says about the gossiper, not so much the subject of the rumor. I took a workshop on this many years ago and it's been very helpful in guiding my own speech and recognizing that things we might consider innocuous aren't. It also helps in dealing with people who are sharing gossip with us. Great for adults and kids.
Mostly, I think you have to get her to recognize her mistake (sounds like she does), feel back about it (sounds like she does), and have a plan for confronting these situations when they occur again (sounds like she doesn't). Whether that includes making amends with the subject of the rumor is up to you, but certainly a pledge to be kinder to the person being talked about or ostracized might help her move on as well as be an example to others. I think you also want to set the stage for her to be able to come to you when she makes a mistake rather than fearing your disappointment. That's important now, and it's going to be absolutely vital in the teen years.
Good luck.